where \(n=n_1 + n_2\) . We denote by \(\pi \left(\cdot \right)= P\left(\delta _{2j}=1 |X_{1j}=\cdot \right)\) , the conditional probability that the observation \(X_{2j}\)  will be missing given \(X_{1j}\) . A natural way to incorporate the missing data mechanism in the test statistic is to associate weight \(\omega _j\)  with the \(j\) -th observation via an inverse probability weighting (IPW) estimator [1]}, given by
\(\omega _j= \frac{\delta _{2j}}{n\pi \left(X_{1j}\right)},~ j = 1,\dots , n.\) 
